Religion separate from state control provides a degree of social cohesion, a sense of communal belonging through shared rituals,common aims. On an individual level it motivates people to make moral decisions, obey laws, contribute to the communal good and gives people a sense of direction and purpose.
Western Europe is a good case- it is overwhelmingly Christian in culture- many political parties in Europe are Christian democrats and religion is a major feature of European societies.
If we stick with Eastern bloc countries they have mostly overthrown their Communist/atheistic governments and now allow religious freedom for people of all faiths.
They overthrew their Communist dictatorships because they were not working on economic or political levels. I hope I've answered your point.